A Splitting Method for Unsteady Incompressible Viscous Fluids Imposing No Boundary Conditions on Pressure

We propose a time-advancing scheme for the discretization of the unsteady incompressible Navier-Stokes equations. At any time step, we are able to decouple velocity and pressure by solving some suitable elliptic problems. In particular, the problem related with the determination of the pressure does not require boundary conditions. The divergence free condition is imposed as a penalty term, according to an appropriate restatement of the original equations. Some experiments are carried out by approximating the space variables with the spectral Legendre collocation method. Due to the special treatment of the pressure, no spurious modes are generated.